Function Graph Selection: Y = X - 8 Relationship Analysis

Q: What does 'Y matches any value of X a number less than it for 8' mean?

This awkward phrasing means Y equals X minus 8, or $ Y = X - 8 $. For any X value, Y will be 8 units smaller.

Q: How do I identify the correct graph for Y = X - 8?

Look for a straight line that crosses the y-axis at -8 and has a slope of 1 (rises 1 unit for every 1 unit right). It should pass through points like (0, -8) and (8, 0).

Q: Why does the line go up from left to right?

Because the slope is positive 1! In $ Y = X - 8 $, the coefficient of X is +1, so the line rises at a 45-degree angle.

Q: What's the difference between Y = X - 8 and Y < 8?

$ Y = X - 8 $ is a diagonal line that can have Y-values above and below 8. \( Y would be a horizontal region below the line Y = 8.

Q: How can I verify I chose the right graph?

Pick two points from your chosen graph and check if they satisfy $ Y = X - 8 $. For example, if the graph shows (10, 2), then 2 = 10 - 8 ✓

Linear Functions with Negative y-intercept

Since Y is a function of X that matches any value of X a number less than it for 8

Circle the appropriate graph to describe the function

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Draw the function graph

00:05 Function equation according to the given data

00:10 Substitute values in X and find the corresponding Y values according to the given data

00:15 Plot each point in our coordinate system

00:20 To draw a graph we need at least 3 points

01:00 Draw the appropriate graph

01:05 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Since Y is a function of X that matches any value of X a number less than it for 8

Circle the appropriate graph to describe the function

Step-by-step solution

We need to determine which graph represents the function $Y = f(X)$ where $Y$ is strictly less than 8 for all $X$ . A key indication is that the function should be a horizontal line or region that does not reach or exceed the line $Y = 8$ .

Reviewing the provided options, look for a graph that closely aligns with being constantly below the line $Y = 8$ . Given the descriptions, a horizontal line at $Y = 7$ or $Y = 6$ would work since it satisfies the inequality $Y < 8$ regardless of the $X$ values.

Option 4 clear depicts a line where all $Y$ -values are indeed less than 8. The graph shows a continuous horizontal segment that stays consistently below 8.

Thus, the graph that correctly describes this function is the one in Choice 4.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Translation: Y equals X minus 8 creates linear function
Pattern: For X = 0, Y = -8; for X = 10, Y = 2
Check: Line passes through (0, -8) and has slope 1 ✓

Common Mistakes

Avoid these frequent errors

Misreading 'less than X for 8' as Y < 8
Don't interpret 'less than X for 8' as Y < 8 = horizontal line below 8! This misses the actual relationship. Always translate 'Y matches X minus 8' as Y = X - 8, creating a diagonal line with negative y-intercept.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

FAQ

Everything you need to know about this question

What does 'Y matches any value of X a number less than it for 8' mean?

This awkward phrasing means Y equals X minus 8, or $Y = X - 8$ . For any X value, Y will be 8 units smaller.

How do I identify the correct graph for Y = X - 8?

Look for a straight line that crosses the y-axis at -8 and has a slope of 1 (rises 1 unit for every 1 unit right). It should pass through points like (0, -8) and (8, 0).

Why does the line go up from left to right?

Because the slope is positive 1! In $Y = X - 8$ , the coefficient of X is +1, so the line rises at a 45-degree angle.

What's the difference between Y = X - 8 and Y < 8?

$Y = X - 8$ is a diagonal line that can have Y-values above and below 8. $Y < 8$ would be a horizontal region below the line Y = 8.

How can I verify I chose the right graph?

Pick two points from your chosen graph and check if they satisfy $Y = X - 8$ . For example, if the graph shows (10, 2), then 2 = 10 - 8 ✓

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